LSTM

it=σ(Wiixt+bii+Whiht−1+bhi)ft=σ(Wifxt+bif+Whfht−1+bhf)gt=tanh⁡(Wigxt+big+Whght−1+bhg)ot=σ(Wioxt+bio+Whoht−1+bho)ct=ft⊙ct−1+it⊙gtht=ot⊙tanh⁡(ct)\begin{array}{ll} \\ i_t = \sigma(W_{ii} x_t + b_{ii} + W_{hi} h_{t-1} + b_{hi}) \\ f_t = \sigma(W_{if} x_t + b_{if} + W_{hf} h_{t-1} + b_{hf}) \\ g_t = \tanh(W_{ig} x_t + b_{ig} + W_{hg} h_{t-1} + b_{hg}) \\ o_t = \sigma(W_{io} x_t + b_{io} + W_{ho} h_{t-1} + b_{ho}) \\ c_t = f_t \odot c_{t-1} + i_t \odot g_t \\ h_t = o_t \odot \tanh(c_t) \\ \end{array}